Measures of Central Tendency
A measure of central tendency is a single number that best represents an entire set of values (either a sample or an entire population). We have three options:
- Mean: the average value, outliers skew this number
- Median: the number in the middle (if there are two in the middle, average those two)
- Mode: the value that appears most often, more useful with categorical variables
Measures of Variability
With measures of variability we want to get one number to represent how spread out or how clumped together the set of values are. Typically, we will look at:
- Range: the minimum and the maximum value of a set of data (also represented as the difference between those two numbers)
- Interquartile range: the 25th and 75th percentile values of a set of data (also represented as the difference between those two numbers)
- Variance: take how far each value is from the mean, square it (to get rid of negative numbers), then average all those differences from the mean. This will result in units that are on a different scale from the original values (and the central tendency). For example, if we are looking at height in inches the variance will be in inches squared.2
- Standard Deviation: the square-root of the variance; the units of this measure of variability will match that of the data set (if we are looking at height in inches, the units of the standard deviation will also be inches)
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